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Extreme waves that appear from nowhere: on the nature of rogue waves. (English) Zbl 1229.76012

Summary: We have numerically calculated chaotic waves of the focusing nonlinear Schrrödinger equation (NLSE), starting with a plane wave modulated by relatively weak random waves. We show that the peaks with highest amplitude of the resulting wave composition (rogue waves) can be described in terms of exact solutions of the NLSE in the form of the collision of Akhmediev breathers.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
35Q30 Navier-Stokes equations
76B25 Solitary waves for incompressible inviscid fluids
35Q55 NLS equations (nonlinear Schrödinger equations)
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